Assignment 1

geom_signif

Illustration

library(ggsignif)
ggplot(iris, aes(x = Species, y = Petal.Length)) +
  geom_boxplot(col="blue") +
  geom_signif(
    comparisons = list(c("setosa", "virginica")),
    map_signif_level = TRUE
  )

geom-crossbar

Various ways of representating a vertical interval defined by x,ymin and ymax.Each case draws a single graphical object.

Illustration

df <- data.frame(
  trt = factor(c(1, 1, 2, 2)),
  resp = c(1, 5, 3, 4),
  group = factor(c(1, 2, 1, 2)),
  upper = c(1.1, 5.3, 3.3, 4.2),
  lower = c(0.8, 4.6, 2.4, 3.6)
)

p <- ggplot(df, aes(trt, resp, colour = group))
p + geom_linerange(aes(ymin = lower, ymax = upper),width = 0.2)

geom_blank

The blank geom draws nothing, but can be a useful way of ensuring common scales between different plots

Illustration

blank <- geom_blank(aes(color = Species), data = iris)
ggplot(iris[iris$Species == "setosa", ]) +
  geom_blank(aes(color = Species), data = iris) +
  geom_point(aes(x = Sepal.Length, y = Petal.Length, color = Species))

geom_sf, geom_sf_text

geom_sf() will draw different geometric objects depending on what sample features are present in the data. We can get points,lines or polygons and for text and labels can use geom_sf_text(). So I am plotting a map using geom_sf() and labeling the features with geom_sf_text().

Illustration

library(ozmaps)
library(sf)

oz_states <- ozmaps::ozmap_states


ggplot() +
  geom_sf(data = oz_states) +
  geom_sf_text(data = oz_states, aes(label = NAME))

geom_tile

geom_tile is geometry layer for rectangles rendering which are defined by the center of rectangle and its size (x,y,width,height).

Illustration

#install.packages(reshape)
library(reshape)

set.seed(8)
m <- matrix(round(rnorm(200), 2), 10, 10)
colnames(m) <- paste("Col", 1:10)
rownames(m) <- paste("Row", 1:10)

df <- melt(m)
colnames(df) <- c("x", "y", "value")

# install.packages("ggplot2")
library(ggplot2)

ggplot(df, aes(x = x, y = y, fill = value)) +
  geom_tile(color = "white",
            lwd = 1.5,
            linetype = 1) +
  coord_fixed()

geom_rug

geom_rug is a compact visualization designed to supplement a 2d display with the two 1d marginal distributions.

Illustration

ggplot(mpg,aes(x=displ,y=cty))+geom_point()+geom_rug(alpha=1/2,position="jitter")

geom_text_repel

geom_text_repel adds text directly to the plot. geom_label_repel draws a rectangle underneath the text, making it easier to read. The text labels repel away from each other and away from the data points.

Illustration

library(ggrepel)
dat2 <- subset(mtcars, wt > 3 & wt < 4)
# Hide all of the text labels.
dat2$car <- ""
# Let's just label these items.
ix_label <- c(2, 3, 14)
dat2$car[ix_label] <- rownames(dat2)[ix_label]

ggplot(dat2, aes(wt, mpg, label = car)) +
  geom_text_repel() +
  geom_point(color = ifelse(dat2$car == "", "grey50", "red"))

dat3 <- rbind(
  data.frame(
    wt  = rnorm(n = 10000, mean = 3),
    mpg = rnorm(n = 10000, mean = 19),
    car = ""
  ),
  dat2[,c("wt", "mpg", "car")]
)

ggplot(dat3, aes(wt, mpg, label = car)) +
  geom_point(data = dat3[dat3$car == "",], color = "grey50") +
  geom_text_repel(box.padding = 0.5, max.overlaps = Inf) +
  geom_point(data = dat3[dat3$car != "",], color = "red")

geom_hdr_boxplot

geom_hdr_boxplot can be used to create boxplot for the highest density region.

Illustration

library(gghdr)
ggplot(trees, aes(x = Girth, y = Volume)) +
  geom_hdr_boxplot(fill="pink") +
  theme()

geom_ribbon

For each x value, geom_ribbon() displays a y interval defined by ymin and ymax. geom_area() is a special case of geom_ribbon(), where the ymin is fixed to 0 and y is used instead of ymax.

Illustration

Year <- 1981:2020
Low <- runif(40,min=50,max = 100)
High <- runif(40,min = 100, max = 200)
ETFValue <- (Low + High)/2
ETFValue <- (Low + High)/2
sample_Data <- data.frame(Year,Low,High,ETFValue)
ggplot(sample_Data,aes(Year))+geom_ribbon(aes(ymin=Low, ymax=High),fill="yellowgreen")+ylab("ETF Value")

geom_image

Illustration

library("ggimage")

set.seed(2017-02-21)
img <- list.files(system.file("extdata", package="ggimage"),
                  pattern="png", full.names=TRUE)
d <- data.frame(x = rnorm(30),
                y = rnorm(30),
                image = sample(img, size=30, replace = TRUE)
)

ggplot(d, aes(x, y)) + geom_image(image=d$image[1])

ggplot(d, aes(x, y)) + geom_image(aes(image=image), size=.06)

d$size=seq(.05, .15, length.out=15)
ggplot(d, aes(x, y)) + geom_image(aes(image=image, size=I(size)))

ggplot(d, aes(x, y)) + geom_image(aes(image=image), color="firebrick")

geom_lm_formula

geom_lm_formula can be use to identify the linear regression function of a given data set.

Illustration

library(mozzie)
library(ggxmean)
ggplot(mozzie, aes(x=Week, y=Colombo))+stat_smooth(method = "lm", Se=F, col="red")+geom_point()+ geom_lm_formula()

geom_density_ridges_gradient

geom_density_ridges_gradient is used to draw lines with a filled area underneath color gradients. . ## Illustration

library(ggridges)
ggplot(lincoln_weather, aes(x = `Mean Temperature [F]`, y = `Month`, fill = stat(x))) +
geom_density_ridges_gradient(scale = 3, rel_min_height = 0.01) +
scale_x_continuous(expand = c(0, 0)) +
scale_y_discrete(expand = c(0, 0)) +
scale_fill_viridis_c(name = "Temp. [F]", option = "C") +
coord_cartesian(clip = "off") +
labs(title = 'Temperatures in Lincoln NE in 2016') +
theme_ridges(font_size = 13, grid = TRUE) +
theme(axis.title.y = element_blank())

geom_density2d

geom_density2d is used to perform a Kernel density estimation using kde2d and display the result with contours. This can be useful for dealing with overplotting.

Illustration

data(iris)
ggplot(iris,aes(x = Sepal.Length, y = Sepal.Width,col = Species)) +
  geom_point()+
  geom_density2d(size=0.5) +
  facet_wrap( ~ Species)

geom_spoke

This is a polar parameterisation of geom_segment(). It is useful when you have variables that describe direction and distance. The angles start from east and increase counterclockwise.

Illustration

set.seed(1)
df <- expand.grid(x=1:10, y=1:10)
df$angle <- runif(100, 0, 2*pi)

ggplot(df, aes(x,y)) + 
  geom_point() + 
  coord_equal() + 
  geom_spoke(aes(angle = angle),
             radius = 0.7, arrow = arrow (length = unit(0.2, "cm")))

geom_lm_fitted

geom_lm_fitted is a statistical models prediction of mean response value when you put the values of the predictors factor levels or components into the model.

Illustration

library(ggxmean)
ggplot(iris,aes(Petal.Length,Petal.Width))+geom_point()+geom_lm_fitted()

geom_beeswarm

The ggbeeswarm package contains a function named geom_beeswarm, which can be used to create a beeswarm in ggplot2. beeswarm geom is a convenient means to offset points within categories to reduce over plotting.

Illustration

#Sample Data
set.seed(1999)
y<- round(rnorm(200),1)
df<- data.frame(y=y,group=sample(c("G1","G2","G3"),size = 200,replace = TRUE))

library(ggbeeswarm)
ggplot(df,aes(x=group,y=y)) + geom_beeswarm(cex=3)

geom_step

geom_step() is based on both geom_path() and geom_line(). geom_path() connects the observations in the order in which they appear in the data. geom_line() connects them in order of the variable on the x axis. geom_step() creates plots connecting points using steps instead of lines. It highlights when exactly the changes occur.The group aesthetic determines which cases are connected together.

The code and plot of order details of a certain store over a time period is given below.

Illustration

library(ggplot2)
client_no <- c(2578,2563,2618,2571,2596,2532,2736,2512,2674,2691)
date <- as.Date(c("2021-01-04","2021-01-24","2021-03-18","2021-05-06","2021-02-13","2021-03-30",
                  "2021-01-15","2021-03-02","2021-04-21","2021-02-19"))
price <- c(10.81,11.09,12.32,11.33,15.17,18.86,16.89,19.53,20.21,22.01)
price_list <- data.frame(date,client_no,price)
ggplot(price_list,aes(x=date,y=price)) + 
  geom_step(linetype=1,color='#d95f02',alpha=1.6)

geom_xy_xymean

geom_xy_xymean() is used to idetify the place point at mean of x and mean of y in the given data set.

Illustration

library(ggxmean)
ggplot(iris,aes(Petal.Length,Petal.Width))+geom_xy_xymean()

geom_lm_conf_int_segments

geom_lm_conf_int_segments can be used to identify the linear relationship of given data set.

Illustration

library(colmozzie)
library(ggxmean)
ggplot(colmozzie,aes(Year,TEM))+geom_lm_conf_int_segments()

geom_ridgeline_gradient

geom_ridgeline_gradient is used to draw lines with a filled area underneath color gradients.

Illustration

# considering iris dataset

  x <- iris[,2]
  y <-  iris[,4]
  height <- iris[,3]

# plot codes
library(ggridges)
  ggplot(, aes(x, y, height = height, group = iris[,5], fill = factor(iris[,5]))) +
  geom_ridgeline_gradient() +
  scale_fill_viridis_d(direction = -1) +
  theme(legend.position = 'bottom')

geom_emoji

This function is used to add emojis to ggplot2.

Illustration

library(emoGG)
library(ggplot2)
Pic <- "1f337"
ggplot(iris, aes(Sepal.Length, Sepal.Width, color = Species)) +
  do.call(geom_emoji, list(emoji = Pic))

geom_tufteboxplot

geom_tufteboxplot() Can be use to draw Tufte Box Plot.Tufte Box plot is just a box plot made minimal and visually appealing.It Provided by ggthemes package.

Illustration

library(ggthemes)
library(ggplot2)
theme_set(theme_tufte())  # from ggthemes

# plot
ggplot(mpg, aes(manufacturer, cty)) + geom_tufteboxplot() + labs(title="Tufte Styled Boxplot of City Mileage grouped by Class of vehicle ",x="Class of Vehicle",y="City Mileage")

geom_mosaic

Create a Mosaic Plot for Dataset.

Illustration

library(ggmosaic)
ggplot(data = titanic) +
  geom_mosaic(aes(x = product(Class), fill = Survived))

geom_pointrange

geom_pointrange can be used to plot means and standard errors

Illustration

ggplot(data = diamonds) +
  geom_pointrange(mapping = aes(x = cut, y = depth),
                  stat = "summary",
                  fun.ymin = min,
                  fun.ymax = max,
                  fun.y = median,
                  fill='blue',
                  color='red',
                  size=0.8)

geom_lm_pred_int

geom_lm_pred_int is can be used for drawing prediction interval for OLS linear model.

Illustration

library(ggxmean)
ggplot(iris,aes(Petal.Length,Petal.Width))+geom_point()+geom_lm_pred_int()

geom_smooth

This geom_smooth() is in the ggplot package and we can use it for adding a trend line over an existing plot.There are different types of smooths that we can do.By default, the trend line that’s added is a LOESS smooth line.Additionally, there are some optional parameters that you can use inside the parenthesis to change the behavior of the function.The geom_smooth function has a large number of optional parameters.Some of them are, mapping, data, span, method, formula, position etc.

Illustration

ggplot(iris, aes(x=Sepal.Length, y=Sepal.Width , col = Species)) + 
  geom_point(shape = 9) +
  geom_smooth(method=lm , col = "black") +
  theme(legend.position = "bottom") +
  labs(title = "Scatter Plot of Sepal. Length vs Sepal.Width", x = "Length of Sepal (cm)" , y = "Width of Sepal (cm)")

geom_bin_2d

Divides the plane into rectangles, counts the number of cases in each rectangle, and then (by default) maps the number of cases to the rectangle’s fill. This is a useful alternative to geom_point() in the presence of over plotting.

Illustration

library(dplyr)
library(ggplot2)
iris_setosa<- filter(iris,Species == "setosa")
ggplot(iris_setosa, aes(x = Sepal.Length,y = Sepal.Width)) + 
geom_bin_2d(bins = 20,binwidth = c(0.1,0.1)) + 
scale_fill_binned(type = "viridis")+
labs(title = "Distribution of Sepal Length vs Sepal Width for Setosa Flower",x = "Sepal Length",y = "Sepal Width")

geom_dotplot

The geom_dotplot geometry can be stacked also along the y axis instead of x. For this purpose is the binaxis property used

Illustration

data("CO2")
sample_plot <- ggplot(CO2,aes(uptake,fill = Plant))

sample_plot + geom_dotplot(binwidth = 3,method ="histodot",stackratio = 1)

geom_linerange

Geometry representing a vertical interval defined by x, ymin, and ymaxEach case draws a single graphical object.

Illustration

df <- data.frame(
  trt = factor(c(1, 1, 2, 2)),
  resp = c(1, 5, 3, 4),
  group = factor(c(1, 2, 1, 2)),
  upper = c(1.1, 5.3, 3.3, 4.2),
  lower = c(0.8, 4.6, 2.4, 3.6))

p <- ggplot(df, aes(trt, resp, colour = group))
p + geom_linerange(aes(ymin = lower, ymax = upper))

geom_curve

geom_segment() draws a straight line between points (x, y) and (xend, yend). geom_curve draws a curved line.

Illustration

#install.packages("dplyr")
library(dplyr)

df <- data_frame(x.to = c( 2, 3, 3, 2,-2,-3,-3,-2),
                 y.to = c( 3, 2,-2,-3,-3,-2, 2, 3),
                 x = 0,
                 y = 0,
                 x_gt_y = abs(x.to) > abs(y.to),
                 xy_sign = sign(x.to*y.to) == 1,
                 x_gt_y_equal_xy_sign = x_gt_y == xy_sign)

ggplot(df) + 
  geom_curve(aes(x = x, y = y, xend = x.to, yend = y.to, color = x_gt_y_equal_xy_sign),
             curvature = 0.75, angle = -45,
             arrow = arrow(length = unit(0.25,"cm"))) + 
  coord_equal() + 
  theme(legend.position = "bottom") +
  xlim(-4, 4) + ylim(-4,4)

geom_mark_ellipse

This geom lets you annotate sets of points via ellipses. The enclosing ellipses are estimated using the Khachiyan algorithm which guarantees an optimal solution within the given tolerance level. As this geom is often expanded it is of lesser concern that some points are slightly outside the ellipsis. The Khachiyan algorithm has polynomial complexity and can thus suffer from scaling issues.

Illustration

library(ggforce)
ggplot(iris,
  aes(x=Sepal.Length,y=Sepal.Width,col=Species))+
  geom_point()+
  geom_mark_ellipse()

geom_density_2d_filled

This is a 2D version of geom_density() . geom_density_2d() draws contour lines, and geom_density_2d_filled() draws filled contour bands.

Illustration

library(ggdensity)

data(iris)
ggplot(iris ,aes(x = Sepal.Length, y= Petal.Length))+geom_density_2d_filled()

geom_violin

geom_violin can be used to observe the distribution of numeric data and are especially to make a comparison of distributions between multiple groups. The peaks, valleys and tails of each group’s density curve can be compared to see where groups are similar or different.

Illustration

ggplot(iris, aes(x=Species, y=Sepal.Length,fill=Species))+
  geom_violin(alpha=0.5)

geom_segment

‘geom_segment()’ draws a straight line between points (x,y) and (xend, yend) ‘geom_curve()’ draws a curved line. See the underlying drawing functions ‘grid::curveGrob()’ for the parameters that cntrol the curve.

Illustration

b<- ggplot(mtcars, aes(wt,mpg))
df <- data.frame(x1=2.62, x2=3.57, y1=21.0, y2=15.0)
b +
  geom_segment(aes(x=x1, y=y1, xend=x2, yend=y2, colour="segment"), data=df)

geom_label

A pie charts represents the data in the circular graph. Each part represents the count or percentage of the observations of a level for the variable. These are helpful to understand the parts to a whole relationship easily. ggplot2 do not provide direct geom to build pie charts. Create the pie charts using ggplot2 verbs. Key function: geom_bar() + coord_polar(). The borders of the pie can be changed with the color argument of the geom_bar. Generally, values or labels are not displayed inside each slide. We can use geom_label, which adds a border around the values. In order to avoid legend displaying letter “a” inside the boxes, we override this behavior with show.legend = FALSE.

Illustration

library(dplyr)    # data manipulation


# caffeine content in different type of coffee drinks in Ben's beans coffee shop per cup

drink <- c ("brewed coffee","caffe latte","caffe mocha","cappucciono","iced brewed coffee","chai latte" )   # type of drink
caffeine <- c (260 ,75, 95, 75, 120, 60)                    # content in milligrams

df <- data.frame(drink,caffeine)

# creating pie chart

ggplot(df, aes(x="" , y= caffeine, fill = drink)) + geom_bar(stat = "identity" , width = 1 , color= "white" )+
  
  geom_label(aes(label = caffeine),
             position = position_stack(vjust = 0.5),
             show.legend = FALSE) +
  coord_polar("y", start = 0) +
  theme_void()    # remove background, numeric labels  

geom_rect

geom_rect is defined by its four sides (xmin, xmax, ymin, ymax), which are all included in the dataset.

Illustration

df <- data.frame(group = rep(c("group1","group2","group3", "group4", "group5", "group6"), each=3),
                 X = paste(letters[1:18]),
                 Y = c(1:18))

ggplot(df, aes(x = X, y = Y)) +
  geom_rect(aes(xmin = X, xmax = dplyr::lead(X), ymin = -0.5, ymax = Inf, fill = group), 
            alpha = 0.5) +
    theme_classic()

geom_freqpolY

Visualize the distribution of a single continuous variable by dividing the x axis into bins and counting the number of observations in each bin. Histograms (geom_histogram()) display the counts with bars; frequency polygons (geom_freqpoly()) display the counts with lines. Frequency polygons are more suitable when you want to compare the distribution across the levels of a categorical variable. A frequency polygon is a line graph of class frequency plotted against class midpoint.It can be obtained by joining the midpoints of the tops of the rectangles in the histogram.

Illustration

ggplot(diamonds,aes(price,colour=cut))+
  geom_freqpoly(binwidth = 500)

geom_vline

This geom allows to annotate the plot with vertical lines.

Illustration

p <- ggplot(mtcars, aes(x= wt, y= mpg)) + geom_point()
p + geom_vline(xintercept=5)

geom_bkde2d

Contours from a 2d density estimate. Perform a 2D kernel density estimation using bkde2D and display the results with contours. This can be useful for dealing with overplotting

Illustration

library(ggalt)

data(faithful)
ggplot(faithful ,aes(x = eruptions, y = waiting))+geom_bkde2d()+geom_point() +
       xlim(0.5, 6) +
       ylim(40, 110)

geom_spiro

This, rather pointless, geom allows you to draw spirograms, as known from the popular drawing toy where lines were traced by inserting a pencil into a hole in a small gear that would then trace around inside another gear. The potential practicality of this geom is slim and it excists mainly for fun and art.

Illustration

library(ggforce)
ggplot()+
  geom_spiro(aes(R=10,r=3,d=5))

geom_text

Text geoms are useful for labeling plots. They can be used by themselves as scatterplots or in combination with other geoms, for example, for labeling points or for annotating the height of bars.

Illustration

ggplot(mtcars, aes(wt, mpg, label = rownames(mtcars),col=cyl,fontface="bold"))+ geom_text(check_overlap = TRUE,vjust = 0, nudge_y = 0.5,angle = 40)

geom_count

This is a variant geom_point() that counts the number of observations at each location,then maps the count to point area.geom_count is always to plot two variables that are not continuous.It is useful when have discrete data with overlapping.

Illustration

#library(readxl)
#insurance<-read_excel("insurance.xlsx")
#ggplot(insurance)+geom_count(mapping = aes(x=region,y=sex,color=region))+labs(title = "Number of observations in each region")

geom_point_interactive

The interactive parameters can be supplied with two ways: As aesthetics with the mapping argument (via aes()). In this way they can be mapped to data columns and apply to a set of geometries. As plain arguments into the geom_*_interactive function. In this way they can be set to a scalar value.

Illustration

library(ggiraph)
library(rvg)

data(iris)
ggplot(iris ,aes(x = Sepal.Length, y= Petal.Length))+geom_point_interactive()

geom_x_mean

geom_x_mean can be used to place point at mean of x.

Illustration

library(ggxmean)
ggplot(iris) + aes(Petal.Length,Petal.Width) + geom_point(col="blue") + geom_x_mean(col="red")

geom_errorbar

Following gives a brief introduction, on the applications of geom_errorbar. geom_errorbar represents a vertical interval. So it can be used to represent the error range associated with an estimated summaryy statistic. In the example discussed below the iris dataset has been used. The error range is considered to be the, (variable mean +/- standard deviation)

Illustration

data_setosa<-iris[1:50,1:5]
setosa_Mean<-c(5.006,3.428,1.462,0.246)

dev_std1 <- sd(iris[1:50,1]) #Standard Deviation of 1st coulmn Sepal Length
dev_std2 <- sd(iris[1:50,2])
dev_std3 <- sd(iris[1:50,3])
dev_std4 <- sd(iris[1:50,4])

setosa_sd<-c(0.3524897,0.3790644,0.173664,0.1053856)

variables <- c('SL', 'SW', 'PL', 'PW')
dat<-data.frame(setosa_Mean, setosa_sd, variables)
p<- ggplot(data=dat,aes(x=variables, y=setosa_Mean, fill=variables))+
  geom_col(width=0.3)+labs(title="Column Plot of Setosa Means",x="Variables",y="Setosa Means")

q <- p + geom_errorbar(aes(ymin=setosa_Mean-setosa_sd , ymax=setosa_Mean+setosa_sd), width=0.15)
q

geom_raster

Sometimes it is needed to visualize a matrix to see sparsity or compare different kind of ordering.It is similar that matlab spy() function.geom_raster() is a special case of geom_tile where tiles are the same size.

Illustration

pp <- function (n,r=4) {
 x <- seq(-r*pi, r*pi, len=n)
 df <- expand.grid(x=x, y=x)
 df$r <- sqrt(df$x^2 + df$y^2)
 df$z <- cos(df$r^2)*exp(-df$r/6)
 df
}

qplot(x, y, data = pp(20), fill = z, geom = "raster")

pp200 <- pp(200)
base <- ggplot(pp200, aes(x, y, fill = z))


df <- expand.grid(x = 0:5, y = 0:5)
df$z <- runif(nrow(df))


ggplot(df, aes(x, y, fill = z)) + geom_raster()

geom_hex

The “geom_hex” function which is available in ggplot2 package divides the plane into regular hexagons,counts the number of cases in each cases and maps the count in each hexagon to hexagon fill. The “geom_hex” function is similar to the function “geom_bin2” which divides the plane into regular rectangles but “geom_hex” overcomes the visual artifacts occurred as a result of regularity of alignment in “geom_bin2”.The “geom_hex” function is also an alternative to “geom_point” in when there is overplotting.

Illustration

You must install the packages hexbin and ggplot2 in order to run the geom_hex function using “install.packages(”hexbin”)“,”install.packages(“ggplot2”)” commands. You can specify the number of bins or binwidth in each direction to control the size of the bins

library(hexbin)

data(diamonds) # an in built data set in ggplot2 package
ggplot(diamonds, aes(carat, price)) + geom_hex()

ggplot(diamonds, aes(carat, price)) + geom_hex(bins = 50)

ggplot(diamonds, aes(carat, price)) + geom_hex(binwidth = c(1,1500))

geom_dotplot

The geom_dotplot geometry can be stacked also along the y axis instead of x. For this purpose is the binaxis property used

Illustration

data("CO2")

sample_plot <- ggplot(CO2,aes(uptake,fill = Plant))

sample_plot + geom_dotplot(binwidth = 3,method ="histodot",stackratio = 1)

geom_dumbbell

the dumbbell plot shows the change between two points in a data set. it helps us to understand the span of data categorically.

Illustration

ylabel <- c("first","second","third")
x1 <- c(1,2,3)
x2 <- c(4,3,5)
datamain <- data.frame(ylabel,x1,x2)
  
library(ggalt)   

ggplot() + geom_dumbbell(data = datamain, 
                         aes(y = ylabel,
                             x = x1, 
                             xend = x2),
                         size = 1.5)